Originally Posted by

**StandardToaster** We've just started doing continuity, limits of functions etc, and I'm not quite sure how to progress.

If we suppose g and h are real-valued functions, defined on some interval (m,n) containing $\displaystyle

x_0

$, and $\displaystyle

\mathop {\lim }\limits_{x \to x_0 } g\left( x \right) = k

$ and $\displaystyle

\mathop {\lim }\limits_{x \to x_0 } h\left( x \right) = l

$.

I want to show that if $\displaystyle

g\left( x \right) < h\left( x \right){\text{ }}\forall x \in \left( {x_0 - \delta ,x_0 + \delta } \right),\delta > 0

$ then $\displaystyle

k \leqslant l

$